Question

If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?

Answer 1

We have the following situation

Let BD be the diameter and diagonal of the circle and the square respectively.

We know that area of the circle

Area of the square

As we know that diagonal of the square is the diameter of the square.

…… (1)

Substituting in equation (1) we get,

Now we will find the ratio of the areas of circle and square.

Now we will simplify the above equation as below,

Therefore, ratio of areas of circle and square is.